The Spring 2018 Colloquium will take place every Wednesday from 4:30 to 5:30 at CMSA, 20 Garden Street, G10.
The schedule below will be updated as speakers are confirmed.
Date…………  Speaker  Title 
02092018 *Friday  Fan Chung
(UCSD) 
Sequences: random, structured or something in between
There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various `randomlike’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems. 
02142018  Zhengwei Liu
(Harvard Physics) 
A new program on quantum subgroups
Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing. 
02212018  Don Rubin
(Harvard) 
Essential concepts of causal inference — a remarkable history
Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of noncompliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis. 
02262018 *Monday  Tom Hou
(Caltech) 
Computerassisted analysis of singularity formation of a regularized 3D Euler equation
Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D NavierStokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate selfsimilar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate selfsimilar solution, which implies the existence of the finite time blowup of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu. 
03072018  Richard Kenyon
(Brown) 
Harmonic functions and the chromatic polynomial
Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam. 
03142018  
03212018  
03282018  Andrea Montanari (Stanford)  A Mean Field View of the Landscape of TwoLayers Neural Networks
Abstract: Multilayer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly nonconvex and highdimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties? We consider a simple case, namely twolayers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain nonlinear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearlyideal generalization error. This description allows to `averageout’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well. 
03302018


04042018  Ramesh Narayan
(Harvard) 
Black Holes and Naked Singularities
Abstract: Black Hole solutions in General Relativity contain Event Horizons and 
04112018  Pablo Parrilo
(MIT) 
Graph Structure in Polynomial Systems: Chordal Networks
Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT). 
04182018  Washington Taylor
(MIT) 
On the fibration structure of known CalabiYau threefolds
Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of Ftheory and new generalized CICY constructions, that a large fraction of known CalabiYau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with YuChien Huang on a systematic analysis of the fibration structure of known toric hypersurface CalabiYau threefolds. Among other results, this analysis shows that every known CalabiYau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of CalabiYau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in CalabiYau threefolds. 
04252018  Xi Yin
(Harvard)

How we can learn what we need to know about Mtheory
Abstract: Mtheory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with superPoincare symmetry and no dimensionless coupling constant. I will review what was known about Mtheory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the Smatrix of Mtheory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of Mtheory from ABJM theory. 
05022018  
05092018 
For information on previous CMSA colloquia, click here.